ALTER TABLE to add a composite primary key

I have a table called provider. I have three columns called person, place, thing. There can be duplicate persons, duplicate places, and duplicate things, but there can never be a dupicate person-place-thing combination.

How would I ALTER TABLE to add a composite primary key for this table in MySQL with the these three columns?

ALTER TABLE provider ADD PRIMARY KEY(person,place,thing);

If a primary key already exists then you want to do this

ALTER TABLE provider DROP PRIMARY KEY, ADD PRIMARY KEY(person, place, thing);

@Adrian Cornish's answer is correct. However, there is another caveat to dropping an existing primary key. If that primary key is being used as a foreign key by another table you will get an error when trying to drop it. In some versions of mysql the error message there was malformed (as of 5.5.17, this error message is still

alter table parent  drop column id;
ERROR 1025 (HY000): Error on rename of
'./test/#sql-a04_b' to './test/parent' (errno: 150).

If you want to drop a primary key that's being referenced by another table, you will have to drop the foreign key in that other table first. You can recreate that foreign key if you still want it after you recreate the primary key.

Also, when using composite keys, order is important. These

1) ALTER TABLE provider ADD PRIMARY KEY(person,place,thing);
and
2) ALTER TABLE provider ADD PRIMARY KEY(person,thing,place);

are not the the same thing. They both enforce uniqueness on that set of three fields, however from an indexing standpoint there is a difference. The fields are indexed from left to right. For example, consider the following queries:

A) SELECT person, place, thing FROM provider WHERE person = 'foo' AND thing = 'bar';
B) SELECT person, place, thing FROM provider WHERE person = 'foo' AND place = 'baz';
C) SELECT person, place, thing FROM provider WHERE person = 'foo' AND place = 'baz' AND thing = 'bar';
D) SELECT person, place, thing FROM provider WHERE place = 'baz' AND thing = 'bar';

B can use the primary key index in ALTER statement 1
A can use the primary key index in ALTER statement 2
C can use either index
D can't use either index

A uses the first two fields in index 2 as a partial index. A can't use index 1 because it doesn't know the intermediate place portion of the index. It might still be able to use a partial index on just person though.

D can't use either index because it doesn't know person.

See the mysql docs here for more information.

You may simply want a UNIQUE CONSTRAINT. Especially if you already have a surrogate key. (example of an already existing surrogate key would be a single column that is an AUTO_INCREMENT )

Below is the sql code for a Unique Constraint

ALTER TABLE `MyDatabase`.`Provider`
    ADD CONSTRAINT CK_Per_Place_Thing_Unique UNIQUE (person,place,thing)
;

alter table table_name add primary key (col_name1, col_name2);

It`s definitely better to use COMPOSITE UNIQUE KEY, as @GranadaCoder offered, a little bit tricky example though:

ALTER IGNORE TABLE table_name ADD UNIQUES INDEX idx_name(some_id, another_id, one_more_id);

ALTER TABLE table_name DROP PRIMARY KEY,ADD PRIMARY KEY (col_name1, col_name2);